1. You flip four coins. Let X, the random variable, be the number of heads on all four coins. H heads. discrete

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1 Statistics Name: Date: Class#: Chapter 4 Practice Discrete Probability Distributions Worksheet You flip four coins Let, the random variable, be the number of heads on all four coins H heads a List the sample space for the experiment F ttails ftppping4coins { #2 HHHHHHHT, TTTT} 2226 b What are the possible values for x? # heads :{ 0,443,43 c Is the random variable, x, continuous or? it 2nd 3rd 4th ( t y a ( ", gt,, d Construct a probability distribution for this experiment P() the e Construct a histogram for the probability distribution in the space below 4/6 2/6 : " 0 l 2 z 4 # heads

2 2 Determine if the following are probability distributions (if no, state why) a P() 4/9 2/9 /9 /9 /9 all prob between 0 AND I 4g to at yes 2 sample space L at at G I b P() 3/0 /0 /0 2/0 3/0 all prob between 0 AND I to to to 2,03,0 Fo L 2 sample space c P() VI not between 0 AND 2 sample space T 25 3 Determine if the following are or continuous random variables: a The speed of a race car in mph Continuous b The number of bottles of Diet Mt Dew that Mr Myers drinks each day c The number of people that play the SC Lottery each day d The weight of a rhinoceros e The time it takes to complete Mr Rich s midterm Continuous f The number of math majors at UCLA g The blood pressures of patients at Lexington Medical Center Continuous

3 4 Construct a probability distribution for the data and draw a histogram for the following: a The probabilities that a patient will have 0,,2, or 3 medical tests performed on entering a hospital are 6/5, 5/5, 3/5, and /5 respectively # tests 0 I 2 3 P() Fs I PA) # Es I 2 3 b A die is loaded in such a way that the probabilities of getting, 2, 3, 4, 5, and 6 are /2, /6, /2, /2, /2, and /2 respectively #dob P() c A box contains three $ bills, two $5 bills, one $0 bill, and one $20 bill P() # Medical tests i E Ei Pan /2 Yz 6 Yr /2 /2 Tz $ $5 $0 $20 F P(x)7 # dots $inb slinbox d A family has three children Let represent the number of boys P() yg 2 3 3/8 3/8 Y8 # boys B( as I 2 3 past B # boys G <, < Fs < 9 B G< <

4 5 Below is a probability distribution for the number of math failures of MHS students P() a P( 2) 00 ( ) 0890 b P( < 2) c P( 2) d P( ) e P( > 2) L P # 2) L 0900,0 f P( 3 or 4) q mutually exclusive yes Mean, Variance, and Expectation 6 From past experience, a company has found that in carton of transistors, 92% contain no defective transistors, 3% contain one defective transistor, 3% contain two defective transistors, and 2% contain three defective transistors a Construct a probability distribution below # defective transistors 0 I 2 3 P() EPCHH? all pk ) between Oand?

5 µ 2) 3) D 3) b Calculate the mean, variance, and standard deviation for the defective transistors E ( ) µ? 0 ( 09 I ( 003 ) 2 ( OO 3) 3 ( defective transistors s 2 ( )(05) 4003 ) ( )( ) 0308 defective transistors 2 s OF 0555 defective transistors 7 The number of suits sold per day at Suit World is shown in the probability distribution below : # suits sold per day P() a Find the mean, variance, and standard deviation of the distribution µ 9 ( 0 2) 20 ( 0 2 ( 0 22 (02)23 ( suits Sold s 2 (9208)<(02)(20208) (02)(2208) suits sold 2 ( )( ) s 249 suits sold b If the manager of Suit World wants to make sure that he has enough suits for the next five days, how many should he buy to stock the store? 208dg 5 (208)04 suits

6 The Bank of America VP feels that each savings account customer has, on average, three credit cards The following distribution represents the number of credit cards people own :# Credit cards people Own P() a Find the mean, variance, and standard deviation µ 0 ( 08 ) I (044)2 (027)3 ( 008 )t4( OO 3) 34 Credit Cards (0345/08) (434)<(003) (234) s 2 ( )2( 044 ) " (334)(008) ( 027 ) OH 0924 credit cards s 096 Credit Cards b Is the VP correct? No, if you were to sample an infinite number of people and ask how many credit cards they own, they would have on average 34 credit cards per person 9 Flower World determines the probabilities for the number of flower arrangements they deliver each day :# flower arrangements delivered per day P() a Find the mean, variance, and standard deviation µ 6 (04702)803 )t9( flower arrangements s 2 flower arrangements " ( )( ) ( )(9076) 404(0076) 40 ) s NOR 3 flower arrangements b Approximately how many arrangements should Flower World expect to deliver each week? E() 076 flower arrangements / day 7 days 7 (076)7532 flower arrangements

7 Cost cost bills Games & Expectation 0 A box contains ten $ bills, %%o% five Yoko $2 bills, three $5 bills, one $0 bill, and one $00 bill A person is charged $20 to select one bill $ a) Define : player gain Pk) b) Find the expected value for this game as if it were free EC) 4%02 (5/20)5 (3/20)0 ( Yzo ) 00 ( Yzo ) 725 dollars c) How much is the true expected value of this game (using the cost)? E ( x ) dollars ( the true ECD d) Interpret what this means in context If people were to play this game an infinite number of times the average gain would be $275 per turn This indicates that the person would lose $275 per turn e) What is the expected gain if 00 people were to play? 00 (275){2750 financing cost f) How much should the game charge to make the game fair? E() without cost 725 dollars If fair, E() cost > charge 725 dollars g) How much should the game charge to make a profit? EC) < 0 anything > 725 dollars h) What is the standard deviation? EC) 725 dollars VARKK (00725%0) ( 7255%(0725%0) Hat#zdifztzsHdf5 dollars dollars

8 If a person rolls doubles when he tosses two dice, he wins $5 The cost to play the game is $ Is this game fair? win lose a) Define : slpiayergain 5 0 PM 436 3%6 b) Find the expected value for this game as if it were free [ 5 (6/360/3936)0833 dollars c) How much is the true expected value of this game (using the cost)? EC) cost dollars d) Interpret what this means in context If people were to play this game an infinite number of times the average gain would be $067 per turn This indicates that the person would lose $067 per turn EK ) host e) What is the expected gain if 00 people were to play? E() lo0fo dollars ) f) How much should the game charge to make the game fair? whenfai R EW Costo Should charge 0833 dollars ( 834 ) g) How much should the game charge to make a profit? Ek ) costco anything more than 0833 dollars h) What is the standard deviation? E()O 833 VARHK ( )( ) 3472 dollars SDI) dollars